Triple

T5570566
Position Surface form Disambiguated ID Type / Status
Subject Fermat's little theorem E146189 entity
Predicate relatedTo P37 FINISHED
Object Euler's theorem E300757 NE FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Euler's theorem | Statement: [Fermat's little theorem, relatedTo, Euler's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euler's theorem
Context triple: [Fermat's little theorem, relatedTo, Euler's theorem]
  • A. Euler’s theorem chosen
    Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
  • B. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • C. de Bruijn–van Aardenne–Ehrenfest theorem
    The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
  • D. Fermat's Last Theorem
    Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
  • E. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69c008ffed108190a084602227af6157 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c020502a288190af37f9ebb88fccae completed March 22, 2026, 5:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0284bb71881908c0ac4ea2a302327 completed March 22, 2026, 5:35 p.m.
Created at: March 22, 2026, 3:37 p.m.